2331_Notes_7o2_fill

2331_Notes_7o2_fill - Math 2331 Linear Algebra Section 7.1...

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Math 2331 Linear Algebra Section 7.1 and 7.2 Linear Transformation Part 2 Linear Transformation Vocabulary - inherited from abstract algebra Kernel - Let T be a linear transformation from the vector space V to the vector space W. The set of all elements v in V that are mapped to the zero vector in W is called the kernel of T. The kernel of T is a subspace of V. Range - The range of the linear transformation T is the set of all possible output values from T. It is a subspace of W. Translate for the matrix A - Kernel - Nullspace of the matrix for the transformation Range - Column Space of the matrix A A Nice Property of Linear Transformations Function Value for the 0 vector - T(0) = 0 Why?

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Example 1: Find the kernel and the range for the transformation - Let be defined by 2 : f \\ 3 2 3 x x f xy y y ⎡⎤ ⎛⎞ ⎢⎥ =− ⎜⎟ ⎣⎦ ⎝⎠
Example 2: Find the kernel and range of the linear transformation - T(x) = Ax for the matrix 120 1 2 001 1 1 000 0 0 A ⎛⎞ ⎜⎟ =− ⎝⎠

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This note was uploaded on 08/10/2011 for the course MATH 2331 taught by Professor Staff during the Spring '08 term at University of Houston.

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2331_Notes_7o2_fill - Math 2331 Linear Algebra Section 7.1...

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